I need a good explanation for this problem please

Question

We’ll call a set of numbers un-average if the average of any two numbers in the set is not in the set. So {1, 3, 6, 7, 10} is un-average, but {1, 3, 6, 7, 9} is not. What is the largest set of un-average numbers whose elements are less than or equal to 10? Less than or equal to 20? Less than or equal to n?

Answer 1

As stated previously, if n is real, there is no maximum (each set can have infinitely many members). If n is restricted to positive integers, then the largest possible set size is 5 (when n=10) and 9 (when n=20). I don't know the general formula.